you can and you do, this is the core principal for electrical motors and Generators.
the issue is more about defeating the inherent inneficiency so that you can have a net positive afterwards you still need to introduce energy ot the system ot have the core spin so it can take advantage of the magnets.
even if you had this motor setup to feed itself the resulting output would be a net negative and it would eventually stop(if this were not the case then there would be a violation of the principle of energy conservation)
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